On Edge-Balance Index Sets of the Graph C_n×P_b(n=0,1,2mod6)

Abstract:

Let G be a simple graph with vertex set V(G) and edge set E(G), and let Z₂=(0,1) For a given binary edge labeling f:E(G)→Z₂,the edge labeling f induces a partial vertex labeling f*:V(G)→Z₂ such that f*(v)=1(0) iff the number of 1-edges (0-edges) is strictly greater than the number of 0-edges (1-edges) incident to , otherwise f*(v) is undefined. For i∈Z₂, let v(i)=card(e∈V(G):f*(v)=i) and e(i)=card(e∈E(G):f(e)=i). The edge-balance index sets of a graph G,EBI(G), is defined as {|v(0)-v(1): the edge labeling f satisfies } . In this paper, we completely determine the edge-balance index |e(0)-e(1)|≤1 sets of the graph C_n×P_b(n=0,1,2 mod 6)

• Periodical: Applied Mechanics and Materials (Volumes 143-144)
• Pages: 750-754
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.143-144.750
• Online since: December 2011
• Authors: Yu Rong Ji, Ying Fang Zhang, Yu Ge Zheng
• Keywords: Edge Labeling, Edge-Balance Index Set, Edge-Friendly

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